# Basics of perfect communication through quantum networks

@article{Kay2011BasicsOP, title={Basics of perfect communication through quantum networks}, author={A. Kay}, journal={Physical Review A}, year={2011}, volume={84}, pages={022337} }

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we… Expand

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Number-theoretic nature of communication in quantum spin systems.

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This work determines the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer and highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and primality. Expand

No Laplacian Perfect State Transfer in Trees

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It is conjecture that perfect state transfer does not happen in trees with more than three vertices, and the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph, is considered. Expand

Quantum Walks and Pretty Good State transfer on Paths

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Quantum computing is believed to provide many advantages over traditional computing, particularly considering the speed at which computations can be performed. One of the challenges that needs to be… Expand

Perfect quantum state transfer using Hadamard diagonalizable graphs

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Abstract Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the… Expand

Two-Excitation Routing via Linear Quantum Channels

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- 2021

It is found that the perturbative transfer scheme allows for efficient two-excitation routing on a fermionic network, although for a spin-$\frac{1}{2}$ network only a limited region of the network is suitable for high-quality routing. Expand

Universality in perfect state transfer

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- 2017

Abstract A continuous-time quantum walk on a graph is a matrix-valued function exp ( − i A t ) over the reals, where A is the adjacency matrix of the graph. Such a quantum walk has universal… Expand

Combinatorial and algebraic aspects of quantum state transfer

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Reliably transferring a quantum state from one location to another, as well as generating entangled states, are important tasks to achieve in quantum spin systems. The fidelity or probability of… Expand

Quantum State Transfer in Graphs

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- 2014

Let X be a graph, A its adjacency matrix, and t ∈ R≥0. The matrix exp(itA) determines the evolution in time of a certain quantum system defined on the graph. It represents a continuous-time quantum… Expand

Communication in Engineered Quantum Networks

- Computer Science
- 2014

We review the engineering of passive quantum networks for performing fundamental quantum communications tasks, such as the transfer, routing, and splitting of signals that are associated with quantum… Expand

Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian

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- 2016

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily… Expand

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